Design of linear time-invariant controllers for multirate systems

In this paper we discuss a frequency domain approach to model multirate single-input single-output (SISO) systems which facilitates design of linear time-invariant (LTI) controllers operating at the fast rate. To illustrate the approach we consider a dual-rate system with slow output measurements and fast control actions. We obtain necessary and sufficient conditions for the existence of stabilizing linear time-invariant (LTI) controllers for which model matching is also achieved at the fast rate with a desired single-rate system. Moreover, a solution to the problem of parameterizing the set of such LTI controllers is also given.     

Verification of reactive systems via instantiation of Parameterised Boolean Equation Systems

Verification problems for finite- and infinite-state processes, like model checking and equivalence checking, can effectively be encoded in Parameterised Boolean Equation Systems (PBESs). Solving the PBES then solves the encoded problem. The decidability of solving a PBES depends on the data sorts that occur in the PBES. We describe a pragmatic methodology for solving PBESs, viz., by attempting to instantiate them to the sub-fragment of Boolean Equation Systems (BESs). Unlike solving PBESs, solving BESs is a decidable problem. Based on instantiation, verification using PBESs can effectively be done fully automatically in most practical cases. We demonstrate this by solving several complex verification problems using a prototype implementation of our instantiation technique. In addition, practical issues concerning this implementation are addressed. Furthermore, we illustrate the effectiveness of instantiation as a transformation on PBESs when solving verification problems involving systems of infinite size.     

New bounded real lemma for discrete-time singular systems

In this paper, the problem of bounded real lemma for discrete-time singular system with strict matrix inequalities is investigated. It is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality. The results lead to more tractable and reliable computation when applying them to design control systems.     

Consistency constraints and 3D building reconstruction

Virtual architectural (indoor) scenes are often modeled in 3D for various types of simulation systems. For instance, some authors propose methods dedicated to lighting, heat transfer, acoustic or radio-wave propagation simulations. These methods rely in most cases on a volumetric representation of the environment, with adjacency and incidence relationships. Unfortunately, many buildings data are only given by 2D plans and the 3D needs varies from one application to another. To face these problems, we propose a formal representation of consistency constraints dedicated to building interiors and associated with a topological model. We show that such a representation can be used for: (i) reconstructing 3D models from 2D architectural plans (ii) detecting automatically geometrical, topological and semantical inconsistencies (iii) designing automatic and semi-automatic operations to correct and enrich a 2D plan. All our constraints are homogeneously defined in 2D and 3D, implemented with generalized maps and used in modeling operations. We explain how this model can be successfully used for lighting and radio-wave propagation simulations.     

Quantifying requirements volatility effects

In an organization operating in the bancassurance sector we identified a low-risk IT subportfolio of 84 IT projects comprising together 16,500 function points, each project varying in size and duration, for which we were able to quantify its requirements volatility. This representative portfolio stems from a much larger portfolio of IT projects. We calculated the volatility from the function point countings that were available to us. These figures were aggregated into a requirements volatility benchmark. We found that maximum requirements volatility rates depend on size and duration, which refutes currently known industrial averages. For instance, a monthly growth rate of 5% is considered a critical failure factor, but in our low-risk portfolio we found more than 21% of successful projects with a volatility larger than 5%. We proposed a mathematical model taking size and duration into account that provides a maximum healthy volatility rate that is more in line with the reality of low-risk IT portfolios. Based on the model, we proposed a tolerance factor expressing the maximal volatility tolerance for a project or portfolio. For a low-risk portfolio its empirically found tolerance is apparently acceptable, and values exceeding this tolerance are used to trigger IT decision makers. We derived two volatility ratios from this model, the π-ratio and the ρ-ratio. These ratios express how close the volatility of a project has approached the danger zone when requirements volatility reaches a critical failure rate. The volatility data of a governmental IT portfolio were juxtaposed to our bancassurance benchmark, immediately exposing a problematic project, which was corroborated by its actual failure. When function points are less common, e.g. in the embedded industry, we used daily source code size measures and illustrated how to govern the volatility of a software product line of a hardware manufacturer. With the three real-world portfolios we illustrated that our results serve the purpose of an early warning system for projects that are bound to fail due to excessive volatility. Moreover, we developed essential requirements volatility metrics that belong on an IT governance dashboard and presented such a volatility dashboard.     

Application of a fault detection filter to structural health monitoring

A model-based fault detection filter is developed for structural health monitoring of a simply supported beam. The structural damage represented in the plant model is shown to decompose into a known fault direction vector maintaining a fixed direction, dependent on the damage location, and an arbitrary fault magnitude representing the extent of the damage. According to detection filter theory, if damage occurs, under certain circumstances the fault will be uniquely detected and identified through an associated invariance in the direction imposed on the fault detection filter residuals. The spectral algorithm used to design the detection filter is based on a left eigenstructure assignment approach which accommodates system sensitivities that are revealed as ill-conditioned matrices formed from the eigenvectors in the construction of the detection filter gains. The detection filter is applied to data from an aluminum simply supported beam with four piezoelectric sensors and one piezoelectric actuator. By exciting the structure at the first natural frequency, damage in the form of a 5 mm saw cut made to one side of the beam is detected and localized.     

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.     

Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions

In this paper, sampled-data control of a set of continuous-time LTI systems is considered. It is assumed that a predefined guaranteed continuous-time quadratic cost function, which is, in fact, the sum of the performance indices for all systems, is given. The main objective here is to design a decentralized periodic output feedback controller with a prespecified form, e.g., polynomial, piecewise constant, exponential, etc., which minimizes the above mentioned guaranteed cost function. This problem is first formulated as a set of matrix inequalities, and then by using a well-known technique, it is reformulated as a LMI problem. The set of linear matrix inequalities obtained provides necessary and sufficient conditions for the existence of a decentralized optimal simultaneous stabilizing controller with the prespecified form (rather than a general form). Moreover, an algorithm is presented to solve the resultant LMI problem. Finally, the efficiency of the proposed method is demonstrated in two numerical examples.     

On using prototype reduction schemes to enhance the computation of volume-based inter-class overlap measures

In most pattern recognition (PR) applications, it is advantageous if the accuracy (or error rate) of the classifier can be evaluated or bounded prior to testing it in a real-life setting. It is also well known that if the two class-conditional distributions have a large overlapping volume (almost all the available work on “overlapping of classes” deals with the case when there are only two classes), the classification accuracy is poor. This is because if we intend to use the classification accuracy as a criterion for evaluating a PR system, the points within the overlapping volume tend to lead to maximal misclassification. Unfortunately, the computation of the indices which quantify the overlapping volume is expensive. In this vein, we propose a strategy of using a prototype reduction scheme (PRS) to approximately, but quickly, compute the latter. In this paper, we demonstrate, first of all, that this is an extremely expedient proposition. Indeed, we show that by completely discarding (we are not aware of any reported scheme which discards “irrelevant” sample (training) points, and which simultaneously attains to an almost-comparable accuracy) the points not included by the PRS, we can obtain a reduced set of sample points, using which, in turn, the measures for the overlapping volume can be computed. The value of the corresponding figures is comparable to those obtained with the original training set (i.e., the one which considers all the data points) even though the computations required to obtain the prototypes and the corresponding measures are significantly less. The proposed method has been rigorously tested on artificial and real-life datasets, and the results obtained are, in our opinion, quite impressive—sometimes faster by two orders of magnitude.     

Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems

This paper investigates simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian (PCH) systems and proposes a number of results on the design of simultaneous stabilization controllers for the PCH systems. Firstly, the case of two PCH systems is studied. Using the dissipative Hamiltonian structural properties, the two systems are combined to generate an augmented PCH system, with which some results on the control design are then obtained. For the case that there exist parametric uncertainties in the two systems’ Hamiltonian structures, an adaptive simultaneous stabilization controller is proposed. When there are external disturbances and parametric uncertainties in the two systems, two simultaneous stabilization controllers are designed for the systems: one is a robust controller and the other is a robust adaptive one. Secondly, the case of more than two PCH systems is investigated, and a new result is proposed for the simultaneous stabilization of the systems. Finally, two illustrative examples are studied by using the results proposed in this paper. Simulations show that the simultaneous stabilization controllers obtained in this paper work very well.